We extend the Standard Model (SM) gauge group by an extra \(U(1)_X\)  under which the SM is neutral. The extra gauge field \(C^{\mu }\)  mixes with the SM \(U(1)_Y\)  hypercharge \(B^{\mu }\) 
via kinetic mixing [1]}.
Further, we use the Stueckelberg mechanism [2]}
to generate mass for the gauge boson of the hidden sector. The total Lagrangian is then given by
\(\mathcal {L}=\mathcal {L}_{\rm SM}+\Delta \mathcal {L},\) 
